Three specific biostatistical inference problems will be investigated in this project. A). Inconducting a clinical trial to compare k treatments, it is desirable balance the trial with respect to the overall assignment of patients to treatments. On the other hand, randomization is essental for reducing experimental bias. Suppose that a restricted randomization scheme was employed in the trial. The problem is how to test the hypothesis of no difference in the effect of the treatments based on the idea of Cox's (1982) Conditional randomization, i.e., the randomization distribution on is taken not over all designs but only over those arrangements with the same or nearly the same terminal lack of balance. B). In a comparative trial, it is impossible to identify and measure all of the covariates of prognostic importance on patients. An important problem is what can be preserved in the assessment of treatment effect without the knowledge of certain covariates when restricted randomization was employed in the trial. C). The principal investigator is interested in obtaining numerical methods to examine the validity of the Cox's proportional hazards model.